All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Just Math
N & n (Posted on 2014-01-27) Difficulty: 2 of 5
N is a m-th power of an integer.
It consists of n distinct digits, averaging n.

Find n,m and N, using your head + pen and paper only.

Check, whether there exist additional solutions (computer allowed).

Clearly, n>1; m>1 - to exclude trivial cases.

No Solution Yet Submitted by Ady TZIDON    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
Looking at my wall | Comment 1 of 7
I found it handy to have tables of exponents and squares on the wall in my classroom.
Looking up there counts as pen and paper IMO.
I see a few three digit examples:
6^3 = 216
12^2 = 144
15^2 = 225
18^2 = 324
21^2 = 441
in each case the sum of digits is 9 and so average 3.

There are obviously no 2 digit examples.
There could be other 3 and 4+ digits examples.

Edit:   I thought of another: 30^2 = 900

Edited on January 27, 2014, 12:44 pm
  Posted by Jer on 2014-01-27 12:42:36

Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (4)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2017 by Animus Pactum Consulting. All rights reserved. Privacy Information